Is the spacetime metric Euclidean rather than Lorentzian?

Understand

My answer to the question in the title is "No".

• In support of this point of view, we analyze some examples of saddle-point methods, especially as applied to quantum "tunneling" in nonrelativistic particle mechanics and in cosmology.
• Along the way we explore some of the interrelationships among different ways of thinking about path-integrals and saddle-point approximations to them.